what are the three coordinates for 4x-3y=-1

Question

be as detailed as possible. Thank you (:

Answer 1

Since  4x-3y=-1  is a line there are actually

an infinite number of points that could be

plotted on the line. 

 

You can find points of the line by picking values for

either variable x or y and solving the equation for

the associated value of the other variable.

 

For example:  If x = 0

4(0) - 3y = -1

-3y = -1

y = 1/3

The point (0, 1/3) is on the line

This is the y-intercept.

 

If y = 0

-4x - 3(0) = -1

-4x = -1

x = 1/4

The point (1/4, 0) is on the line

This is the x-intercept

 

You could conceivably do this for infinite points.

 

For a 3rd point pick another number:

What is y if x = 1

 

4(1)-3y=-1

4 + -3y = -1

-3y = -5

y = 5/3

The point (1, 5/3) is on the line.

***************************************

 

As Michael showed, the slope of the line is m = 4/3

which is the rise/run or (change in y)/(change in x)

 

You can use his method of finding one point and from

that finding another point by adding 4 to the y term

and adding 3 to the x term.

 

From (1, 5/3) → (1+3, 5/3 + 4) = (4, 17/3)

And so forth.

Answer 2

First, we want to put this equation in slope intercept form.  That is y=mx+b, where m is slope and b is y-intercept.
 
 
Subtract 4 on both sides of the equation.
 
-3y = -4x - 1
 
 
Divide both sides of the equation by -3.
 
y = (4 / 3)x + (1 / 3)
 
 
The first point we can plot will be the y-intercept.  The y-intercept is (0, 1/3).
 
 
Next, we can use the slope to find the other 2 points.  From the y-intercept, move 3 units to the right and 4 units up.
 
Second point is (3, 13/3).
 
 
From the second point, use the slope to find the third point.
 
Third point is (6, 25/3).

Answer 3

First, we want to put this equation in slope intercept form.  That is y=mx+b, where m is slope and b is y-intercept.

 

 

Subtract 4 on both sides of the equation.

 

-3y = -4x - 1

 

 

Divide both sides of the equation by -3.

 

y = (4 / 3)x + (1 / 3)

 

 

The first point we can plot will be the y-intercept.  The y-intercept is (0, 1/3).

 

 

Next, we can use the slope to find the other 2 points.  From the y-intercept, move 3 units to the right and 4 units up.

 

Second point is (3, 13/3).

 

 

From the second point, use the slope to find the third point.

 

Third point is (6, 25/3).